541 research outputs found
Optimal entanglement witnesses for continuous-variable systems
This paper is concerned with all tests for continuous-variable entanglement
that arise from linear combinations of second moments or variances of canonical
coordinates, as they are commonly used in experiments to detect entanglement.
All such tests for bi-partite and multi-partite entanglement correspond to
hyperplanes in the set of second moments. It is shown that all optimal tests,
those that are most robust against imperfections with respect to some figure of
merit for a given state, can be constructed from solutions to semi-definite
optimization problems. Moreover, we show that for each such test, referred to
as entanglement witness based on second moments, there is a one-to-one
correspondence between the witness and a stronger product criterion, which
amounts to a non-linear witness, based on the same measurements. This
generalizes the known product criteria. The presented tests are all applicable
also to non-Gaussian states. To provide a service to the community, we present
the documentation of two numerical routines, FULLYWIT and MULTIWIT, which have
been made publicly available.Comment: 14 pages LaTeX, 1 figure, presentation improved, references update
Majorana dimers and holographic quantum error-correcting codes
Holographic quantum error-correcting codes have been proposed as toy models that describe key aspects of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. In this work, we introduce a versatile framework of Majorana dimers capturing the intersection of stabilizer and Gaussian Majorana states. This picture allows for an efficient contraction with a simple diagrammatic interpretation and is amenable to analytical study of holographic quantum error-correcting codes. Equipped with this framework, we revisit the recently proposed hyperbolic pentagon code (HyPeC). Relating its logical code basis to Majorana dimers, we efficiently compute boundary-state properties even for the non-Gaussian case of generic logical input. The dimers characterizing these boundary states coincide with discrete bulk geodesics, leading to a geometric picture from which properties of entanglement, quantum error correction, and bulk/boundary operator mapping immediately follow. We also elaborate upon the emergence of the Ryu-Takayanagi formula from our model, which realizes many of the properties of the recent bit thread proposal. Our work thus elucidates the connection among bulk geometry, entanglement, and quantum error correction in AdS/CFT and lays the foundation for new models of holography
Quantum network routing and local complementation
Quantum communication between distant parties is based on suitable instances of shared entanglement. For efficiency reasons, in an anticipated quantum network beyond point-to-point communication, it is preferable that many parties can communicate simultaneously over the underlying infrastructure; however, bottlenecks in the network may cause delays. Sharing of multi-partite entangled states between parties offers a solution, allowing for parallel quantum communication. Specifically for the two-pair problem, the butterfly network provides the first instance of such an advantage in a bottleneck scenario. In this paper, we propose a more general method for establishing EPR pairs in arbitrary networks. The main difference from standard repeater network approaches is that we use a graph state instead of maximally entangled pairs to achieve long-distance simultaneous communication. We demonstrate how graph-theoretic tools, and specifically local complementation, help decrease the number of required measurements compared to usual methods applied in repeater schemes. We examine other examples of network architectures, where deploying local complementation techniques provides an advantage. We finally consider the problem of extracting graph states for quantum communication via local Clifford operations and Pauli measurements, and discuss that while the general problem is known to be NP-complete, interestingly, for specific classes of structured resources, polynomial time algorithms can be identified
Renormalization algorithm with graph enhancement
We introduce a class of variational states to describe quantum many-body
systems. This class generalizes matrix product states which underly the
density-matrix renormalization group approach by combining them with weighted
graph states. States within this class may (i) possess arbitrarily long-ranged
two-point correlations, (ii) exhibit an arbitrary degree of block entanglement
entropy up to a volume law, (iii) may be taken translationally invariant, while
at the same time (iv) local properties and two-point correlations can be
computed efficiently. This new variational class of states can be thought of as
being prepared from matrix product states, followed by commuting unitaries on
arbitrary constituents, hence truly generalizing both matrix product and
weighted graph states. We use this class of states to formulate a
renormalization algorithm with graph enhancement (RAGE) and present numerical
examples demonstrating that improvements over density-matrix renormalization
group simulations can be achieved in the simulation of ground states and
quantum algorithms. Further generalizations, e.g., to higher spatial
dimensions, are outlined.Comment: 4 pages, 1 figur
Local-channel-induced rise of quantum correlations in continuous-variable systems
It was recently discovered that the quantum correlations of a pair of
disentangled qubits, as measured by the quantum discord, can increase solely
because of their interaction with a local dissipative bath. Here, we show that
a similar phenomenon can occur in continuous-variable bipartite systems. To
this aim, we consider a class of two-mode squeezed thermal states and study the
behavior of Gaussian quantum discord under various local Markovian non-unitary
channels. While these in general cause a monotonic drop of quantum
correlations, an initial rise can take place with a thermal-noise channel.Comment: 6 pages, 4 figure
Quantum mechanics gives stability to a Nash equilibrium
We consider a slightly modified version of the Rock-Scissors-Paper (RSP) game
from the point of view of evolutionary stability. In its classical version the
game has a mixed Nash equilibrium (NE) not stable against mutants. We find a
quantized version of the RSP game for which the classical mixed NE becomes
stable.Comment: Revised on referee's criticism, submitted to Physical Review
Limitations of quantum computing with Gaussian cluster states
We discuss the potential and limitations of Gaussian cluster states for
measurement-based quantum computing. Using a framework of Gaussian projected
entangled pair states (GPEPS), we show that no matter what Gaussian local
measurements are performed on systems distributed on a general graph, transport
and processing of quantum information is not possible beyond a certain
influence region, except for exponentially suppressed corrections. We also
demonstrate that even under arbitrary non-Gaussian local measurements, slabs of
Gaussian cluster states of a finite width cannot carry logical quantum
information, even if sophisticated encodings of qubits in continuous-variable
(CV) systems are allowed for. This is proven by suitably contracting tensor
networks representing infinite-dimensional quantum systems. The result can be
seen as sharpening the requirements for quantum error correction and fault
tolerance for Gaussian cluster states, and points towards the necessity of
non-Gaussian resource states for measurement-based quantum computing. The
results can equally be viewed as referring to Gaussian quantum repeater
networks.Comment: 13 pages, 7 figures, details of main argument extende
Entangled inputs cannot make imperfect quantum channels perfect
Entangled inputs can enhance the capacity of quantum channels, this being one
of the consequences of the celebrated result showing the non-additivity of
several quantities relevant for quantum information science. In this work, we
answer the converse question (whether entangled inputs can ever render noisy
quantum channels have maximum capacity) to the negative: No sophisticated
entangled input of any quantum channel can ever enhance the capacity to the
maximum possible value; a result that holds true for all channels both for the
classical as well as the quantum capacity. This result can hence be seen as a
bound as to how "non-additive quantum information can be". As a main result, we
find first practical and remarkably simple computable single-shot bounds to
capacities, related to entanglement measures. As examples, we discuss the qubit
amplitude damping and identify the first meaningful bound for its classical
capacity.Comment: 5 pages, 2 figures, an error in the argument on the quantum capacity
corrected, version to be published in the Physical Review Letter
Creating and probing macroscoping entanglement with light
We describe a scheme showing signatures of macroscopic optomechanical
entanglement generated by radiation pressure in a cavity system with a massive
movable mirror. The system we consider reveals genuine multipartite
entanglement. We highlight the way the entanglement involving the inaccessible
massive object is unravelled, in our scheme, by means of field-field quantum
correlations.Comment: 4 pages, 5 figure, RevTeX
Dynamics of entanglement of bosonic modes on symmetric graphs
We investigate the dynamics of an initially disentangled Gaussian state on a
general finite symmetric graph. As concrete examples we obtain properties of
this dynamics on mean field graphs of arbitrary sizes. In the same way that
chains can be used for transmitting entanglement by their natural dynamics,
these graphs can be used to store entanglement. We also consider two kinds of
regular polyhedron which show interesting features of entanglement sharing.Comment: 14 pages, 11 figures, Accepted for publication in Physics Letters
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